Details

sample44.0ms

Algorithm

intervals

Results

11.0ms	204×	body	80	valid
7.0ms	24×	body	2560	valid
6.0ms	11×	body	1280	valid
5.0ms	256×	pre	80	true
1.0ms	7×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 10.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* (* 4.0 p) p) (* x x))
268.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify92.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	242	529
1	853	492
2	2977	488
3	5002	487

prune189.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 9.8b

Counts

64 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
1.4b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
1.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-log-exp`
8×	`add-cube-cbrt` `exp-prod`
6×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `log-prod` `add-cbrt-cube`
3×	`sqrt-prod` `distribute-lft-out`
2×	`flip3-+` `sqrt-div` `exp-sum` `sum-log` `flip-+` `rem-exp-log`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 58

Calls

4 calls:

13.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
264.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
82.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify116.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	202	567
1	613	507
2	1609	506
3	3883	506
4	5001	506

prune207.0ms

Filtered

70 candidates to 55 candidates (78.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	68	12	80

Merged error: 9.8b

Counts

80 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
5.4b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
16×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`flip3-+` `sqrt-div` `cube-prod` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `sum-cubes` `div-inv`

Counts

4 → 98

Calls

4 calls:

37.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
50.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	352	1043
1	1550	965
2	5001	964

prune425.0ms

Filtered

110 candidates to 81 candidates (73.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 9.8b

Counts

122 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
5.4b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`log-pow`
9×	`add-exp-log` `exp-prod`
8×	`associate-/l*`
7×	`pow1`
6×	`sqrt-prod` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`log-prod` `sqrt-div` `cube-prod` `unpow2` `add-log-exp` `sqr-pow`
3×	`flip3-+` `div-exp` `associate-/r*` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `rem-log-exp` `exp-sum` `pow-exp` `clear-num` `sum-cubes` `div-inv`

Counts

4 → 103

Calls

4 calls:

39.0ms	(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(log (exp (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))))
51.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
52.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	338	1056
1	1380	962
2	5001	961

prune425.0ms

Filtered

115 candidates to 82 candidates (71.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	115	13	128

Merged error: 9.8b

Counts

128 → 13

regimes303.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	49
1	42	49

end0.0ms

sample1.1s

Algorithm

intervals

Results

314.0ms	6010×	body	80	valid
267.0ms	838×	body	2560	valid
148.0ms	589×	body	1280	valid
146.0ms	8000×	pre	80	true
63.0ms	315×	body	640	valid
27.0ms	165×	body	320	valid
8.0ms	83×	body	160	valid

Details

sample44.0ms

simplify9.0ms

prune2.0ms

localize11.0ms

rewrite34.0ms

series440.0ms

simplify92.0ms

prune189.0ms

localize15.0ms

rewrite44.0ms

series561.0ms

simplify116.0ms

prune207.0ms

localize21.0ms

rewrite58.0ms

series238.0ms

simplify55.0ms

prune425.0ms

localize25.0ms

rewrite60.0ms

series240.0ms

simplify52.0ms

prune425.0ms

regimes303.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling